Hi,
today?s image in fact is more an image then
a fractal. But you?re going to like it.
It?s a very fast one for a change, although
not the fastest by far.
Albrecht
--------------------start-par------------------------
1536709A { ; Crosswise
; Time 0.01.35 1600/1200
; sec-mmods-bees-phoen-spid
reset=2004 type=formula formulafile=mfr_10.frm
formulaname=multifractal_10
function=sin/exp/exp/sin passes=t
center-mag=-1.46373607365559400/-0.000000044867182\
47/154931/1/90/3.88578058618804789e-016
params=-0.05825983458967864/0.3785210730307932/153\
67.64595767025/14235.4911030602/152048.0404808048/\
384.1604894048/384.00482000595/256.1007683001/512.\
1007683001/768.1007683001 float=y maxiter=3071
inside=maxiter outside=tdis periodicity=0
rseed=-2436
colors=000t2tv2u<3>c5eZ6`U6X<2>F9LAAG7FO4KW0Qc<3>5\
Xc6Zc7`c7aa7c_7eY<3>FcgHciJbl<3>S_v<3>civflvinvlqv\
otvsww<2>zzz<3>rwzovzhsw<3>Gch8_d8Xa<3>8JP8FL8CI<4\
>XCAaB9fB7<3>zA0<13>SA1QA1NA1<3>D92<6>UXAW`BYcC<3>\
hrI<3>UnXRm_NlcJkgFfpAaz<3>PJoSFlWAi_5fc0ce7_jFR00\
0oNIzb0<2>zz1zzC<2>zzz<3>jqdfo_blU<3>Mb8<3>LQ8KM8K\
J8<2>I88H44G00<3>TA5WD6ZF7aI8eLAhMBiODjQF<3>qeBriA\
tm9vq8xu7zz5zz4zz3<8>zY4zV5zS5<3>zE6wE6tD6<10>w8Px\
8Rx7S<3>z5_<3>f5Ma5IW4E<2>_4H<3>P3DN2CK2A<3>805G0B\
O0G<3>g0Ul0Xq0`v0d<2>y0fz0gy0h<5>s1or2qs2r
}
frm:multifractal_10 { ; Albrecht Niekamp Jan2005
;RP2 Left: 5 Digits_Channel:1_main 2_outside 3_inside1 4_inside2 5_inside3
; Frms: 0_off 1_Sec 2_Mand(2) 3_Bees 4_Jul 5_Mmod 6_Phoen 7_Newt 8_Spid
; Right: 2 Digits_MMods_Number of sides 2 Dig_Phoenix 2 Dig_Spider
; 1 Dig_TransReset_main :0_no 1_dblmand 2_Iter-res 3_both +5_warp
; 4 Dig_TransReset_Ch2-5:0_no 1_z-reset 2_Iter-res 3_both +5_warp
;IP2 Left: 5 Digits_Bailout Number for Channels 1 to 5
; Right: Variab: 4 Digits_Mand/Jul(2 var) 2 Digits_Secant 4 Digits_Bees
;RP3 Left: 2 Digits_Newtonvariable 4 Digits_Colour1
; Right: 5 Digits_Colour2 5 Digits_Colour3
;IP3 Left: Main: 5 Digits_Warp-factor (fn1 is used)
; Right: 5 Digits_Colour4 6 Digits_Colour5
;RP4 Left: Outside: 5 Digits_Warp-factor (fn2 is used)
; Right: Outside: 4 Dig+1 fractaldig_bord-out 4 Dig+1 fractaldig_bord-in
;IP4 Left: Inside1_Maxiter
; Right: Inside1_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord
; 5 Digits_Warp-factor (fn2 used) 4 Dig+1 fractaldig_border1
;RP5 Left: Inside2_Maxiter
; Right: Inside2_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord
; 5 Digits_Warp-factor (fn3 used) 4 Dig+1 fractaldig_border2
;IP5 Left: Inside3_Maxiter
; Right: Inside3_Transition: 1_maxit 2_bordout 3_bordin +5_maxit+bord
; 5 Digits_Warp-factor (fn4 used) 4 Dig+1 fractaldig_border3
; Altnat: Left: 1_Lake effect enabled (Inside3 disabled)
; Right: 2 Digit_Frequency 2 Digit_Waterlevel 2 Digit_Amplitude
;
le=0
z=pixel
da=real(p2)
dd=trunc(da)
da=round((da-dd)*100000000000)+11111
dd=dd+11111
d=trunc(dd/10000)
dd=dd-d*10000
d3=(d==4)+(d==5)+(d==8)+(d==9)
d4=d3==0
vb=d>5
sc=d==2
mo=d==6
px=d==7
ab=px+(d==3)+(d==5)+(d==9)
d=trunc(dd/1000)
dd=dd-d*1000
ex1=d>1
sc1=d==2
mo1=d==6
px1=d==7
v1m=mo1+px1
v1j=d>7
dd1=v1j+(d==4)+(d==5)
ab1=px1+(d==3)+(d==5)+(d==9)
d=trunc(dd/100)
dd=dd-d*100
ex2=d>1
sc2=d==2
mo2=d==6
px2=d==7
v2m=mo2+px2
v2j=d>7
dd2=v2j+(d==4)+(d==5)
ab2=px2+(d==3)+(d==5)+(d==9)
d=trunc(dd/10)
ex3=d>1
sc3=d==2
mo3=d==6
px3=d==7
v3m=mo3+px3
v3j=d>7
dd3=v3j+(d==4)+(d==5)
ab3=px3+(d==3)+(d==5)+(d==9)
d=dd-d*10
ba=imag(p5)
mi3=trunc(ba)
dd=(d>1)+(mi3>1)
ex4=dd==2
sc4=d==2
mo4=d==6
px4=d==7
v4m=mo4+px4
v4j=d>7
dd4=v4j+(d==4)+(d==5)
ab4=px4+(d==3)+(d==5)+(d==9)
;
mm=trunc(da/1000000000)
da=da-mm*1000000000
ph=trunc(da/10000000)/100
da=da-ph*1000000000
sp=trunc(da/100000)/100
da=da-sp*10000000
d=trunc(da/10000)
ex0=d>4
da=da-d*10000
d=d-5*ex0
dm=(d==2)+(d==4)
ir0=(d==3)+(d==4)
d=trunc(da/1000)
w1=d>4
da=da-d*1000
d=d-5*w1
rs1=(d==2)+(d==4)
ir1=(d==3)+(d==4)
d=trunc(da/100)
w2=d>4
da=da-d*100
d=d-5*w2
rs2=(d==2)+(d==4)
ir2=(d==3)+(d==4)
d=trunc(da/10)
w3=d>4
da=da-d*10
d=d-5*w3
rs3=(d==2)+(d==4)
ir3=(d==3)+(d==4)
d=round(da)
w4=d>4
d=d-5*w4
rs4=(d==2)+(d==4)
tt=ex1+ex0+ex2+ex3+ex4
;
d=real(p3)
dd=trunc(d)
da=(d-dd)*10000000000
pp=trunc(dd/10000)
ba1=dd-10000*pp
ba2=trunc(da/100000)
ba3=da-100000*ba2
;
d=imag(p3)
sfac=trunc(d)
da=(d-sfac)*100000000000
ba4=trunc(da/1000000)
ba5=da-ba4*1000000
;
d=real(p4)
ofac=trunc(d)
da=(d-ofac)*10000000000
bh=trunc(da/100000)/10
bl=(da-bh*1000000)/10
bs=bl/2
;
d=imag(p2)
t=d<0
if (t)
d=-d
endif
dd=trunc(d)
da=round((d-dd)*10000000000)
d=trunc(dd/10000)
dd=dd-d*10000
bb0=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/1000)
dd=dd-d*1000
bb1=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/100)
dd=dd-d*100
bb2=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=trunc(dd/10)
dd=dd-d*10
bb3=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
d=round(dd)
bb4=ba1*(d==1)+ba2*(d==2)+ba3*(d==3)+ba4*(d==4)+ba5*(d==5)
;
d=da
p0=trunc(d/100000000)/10
d=d-p0*1000000000
p6=trunc(d/1000000)/10
d=d-p6*10000000
if (t)
p6=-p6
endif
p7=trunc(d/10000)/10
d=d-p7*100000
dp=p6+p0/100
p8=trunc(d/100)/100
d=d-p8*10000
p9=d/100
;
d=imag(p4)
mi1=trunc(d)
da=(d-mi1)*100000000000
d=trunc(da/10000000000)
bt1=d>6
da=da-d*10000000000
d=d-5*bt1
dt1=d>1
iv1=d==3
fac1=trunc(da/100000)
da=da-fac1*100000
bo1=(da/100000)/10
;
d=real(p5)
mi2=trunc(d)
da=(d-mi2)*100000000000
d=trunc(da/10000000000)
bt2=d>6
da=da-d*10000000000
d=d-5*bt2
dt2=d>1
iv2=d==3
fac2=trunc(da/100000)
da=da-fac2*100000
bo2=(da/100000)/10
;
if (mi3==1)
d=(ba-mi3)*1000000
fr=round((trunc(d/10000))*10) ;lake effect by S.Gallet
d=d-fr*1000
lv=(trunc(d/100))/100
d=d-lv*10000
am=d/100
u=real(rotskew*pi/180)
t=exp(-flip(u))
bo=1/real(magxmag)
q=bo/0.75*imag(magxmag)
dd=tan(imag(rotskew*pi/180))
da=2*q*t
rs=2*bo*(dd+flip(1))*t
zz=center+(-q-bo*dd-flip(bo))*t
z=z-zz
d=imag(conj(da)*z)/imag(conj(da)*rs)
le=d<=lv
if (le)
dd=lv-d
z=z+2*dd*(1+am*sin(fr*dd^0.2))*rs
endif
z=z+zz
else
da=(ba-mi3)*100000000000
d=trunc(da/10000000000)
bt3=d>6
da=da-d*10000000000
d=d-5*bt3
dt3=d>1
iv3=d==3
fac3=trunc(da/100000)
da=da-fac3*100000
bo3=(da/100000)/10
endif
;
if (vb)
if (d3)
if (ab)
z=z*le+pixel*(le==0) ;Spider
c=p1
else
z=z*le+pixel*(le==0)
c=p1 ;newton
endif
elseif (ab)
c=z ;Phoenix
z=z*le+pixel*(le==0)
else
c=0.4*log(sqr(z^mm)) ;many mods
z=0
endif
elseif (d3)
if (ab)
c=p1 ;Julia
z=z*le+pixel*(le==0)
else ;bees
c=p1
z=z*le+pixel*(le==0)
endif
elseif (ab)
c=z ;Mandel
z=0
else
c=z ;Secant
z=z*le+pixel*(le==0)
endif
t=0
bo=|z|
p=pp
z0=p7
zold=(0.0,0.0)
cb=p9
ba=bb0
:
if (tt)
t=t+1
if (ex0)
ex0=t<mi1
if (bo>bs)
u=2*(fn1(t/sfac))
ex0=0
if (ir0)
t=0
endif
if (d4)
z=z*u
if (mo)
c=0.4*log(sqr(z^mm))
else
c=pixel
endif
else
z=z*le+pixel*(le==0)
cb=p9*u
c=p1*u
p=pp*u
endif
tt=tt-1+ex0
endif
elseif ((ex1)&&bo>bl)
if (bo<bh)
d3=dd1
ba=bb1
ab=ab1
ex1=0
tt=tt-1
if (w1)
u=2*(fn2(t/ofac))
else
u=1,0
endif
if (ir1)
t=0
endif
if (d3)
vb=v1j
if (rs1)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
c=p1
z=z*u
cb=p9
endif
else
vb=v1m
if (rs1)
c=z*u
z=pixel*(sc1+px1)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo1)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex2)
if (dt1)
if (iv1)
d=bo>bo1
else
d=bo<bo1
endif
if (bt1)
d=d+(t>mi1)
endif
else
d=t>mi1
endif
if (d)
ab=ab2
d3=dd2
ba=bb2
ex2=0
tt=tt-1
if (w2)
u=2*(fn2(t/fac1))
else
u=1,0
endif
if (ir2)
t=0
endif
if (d3)
vb=v2j
if (rs2)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v2m
if (rs2)
c=z*u
z=pixel*(sc2+px2)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo2)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex3)
if (dt2)
if (iv2)
d=bo>bo2
else
d=bo<bo2
endif
if (bt2)
d=d+(t>mi2)
endif
else
d=t>mi2
endif
if (d)
ab=ab3
d3=dd3
ba=bb3
ex3=0
tt=tt-1
if (w3)
u=2*(fn3(t/fac2))
else
u=1,0
endif
if (ir3)
t=0
endif
if (d3)
vb=v3j
if (rs3)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v3m
if (rs3)
c=z*u
z=pixel*(sc3+px3)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
vb=v3m
if (mo3)
c=0.4*log(sqr(z^mm))
endif
endif
endif
elseif (ex4)
if (dt3)
if (iv3)
d=bo>bo3
else
d=bo<bo3
endif
if (bt3)
d=d+(t>mi3)
endif
else
d=t>mi3
endif
if (d)
ab=ab4
d3=dd4
ba=bb4
ex4=0
tt=0
if (w4)
u=2*(fn4(t/fac3))
else
u=1,0
endif
if (d3)
vb=v4j
if (rs4)
z=pixel
cb=p9*u
c=p1*u
p=pp*u
else
cb=p9
c=p1
z=z*u
endif
else
vb=v4m
if (rs4)
c=z*u
z=pixel*(sc4+px4)
z0=p7*u
ph=ph*u
else
c=z
z=z*u
endif
if (mo4)
c=0.4*log(sqr(z^mm))
endif
endif
endif
endif
endif
if (vb)
if (d3)
if (ab)
z=z*z+c ;Spiderjul John Horner
c=c*sp+z
else
z1=z^p-1 ;Quasinewton Puskas Istvan
z2=p*z*z
z=z-z1/z2
endif
elseif (ab)
z1=z*z+0.56+ph/100-0.5*zold ;Phoenix Mike Wareman
zold=z
z=z1
else
z2=fn1(z)+c ;Many_mods Linda Allison
z1=cos(z2)
z=c*(1-z1)/(1+z1)
endif
elseif (d3)
if (ab)
z2=z*z ;Julia Puskas Istvan
z=z2*z2+p6*z2+c-p0
else
z1=fn1(z)-cb ;Bees Ray Girvan
z2=z1^p8-1
z3=p8*(z1^(p8-1))
z=z-(z2/z3)
endif
elseif (ab)
if (dm)
z=z*z+c+c*c-dp ;Double Mandel
else
z2=z*z ;Mandel Puskas Istvan
z=z2*z2+p6*z2+c-p0
endif
else
z3=z ;Secant Mike Wareman
z1=z0*z0*z0*z0-1
z2=z*z*z*z-1
z=z-z2*(z-z0)/(z2-z1)
z0=z3
endif
bo=|z|
bo<ba
}
---------------------------------end-------------------------------------
